In a University out of 120 students, 15 opted mathematics only, 16 opted statistics only, 9 opted physics only and 45 opted physics and mathematics, 30 opted physics and statistics, 8 opted mathematics and statistics, and 80 opted physics.
Find the sum of number of students who opted mathematics and those who didn't opted any of the subjects given.
+26367 In a University out of 120 students, 15 opted mathematics only, 16 opted statistics only, 9 opted physics only and
45 opted physics and mathematics, 30 opted physics and statistics, 8 opted mathematics and statistics, and
80 opted physics.
Find the sum of number of students who opted mathematics and those who didn't opted any of the subjects given.
My attempt:
\(\begin{array}{|rcll|} \hline x+y+t+9 &=& 80 \quad | \quad x+y = 45 \\ 45+t+9 &=& 80 \\ t+54 &=& 80 \\ t &=& 80-54 \\ \mathbf{ t } &=& \mathbf{26} \\ \hline \end{array} \begin{array}{|rcll|} \hline 30 &=& y+t \\ -~~8 &=& y+z \\ \hline 22 &=& y+t-(y+z) \\ 22 &=& y+t-y-z \\ 22 &=& t-z \\ z+22 &=& t \\ \mathbf{ z } &=& \mathbf{t-22} \quad | \quad \mathbf{ t =26} \\ z &=& 26-22 \\ \mathbf{ z } &=& \mathbf{4} \\ \hline \end{array} \)
\(\begin{array}{|rcll|} \hline z+y &=& 8 \\ y &=& 8-z \quad | \quad \mathbf{z=4} \\ y &=& 8-4\\ \mathbf{ y } &=& \mathbf{4} \\ \hline \end{array} \begin{array}{|rcll|} \hline x+y &=& 45 \\ x &=& 45-y \quad | \quad \mathbf{y=4} \\ x &=& 45-4\\ \mathbf{ x } &=& \mathbf{41} \\ \hline \end{array}\)
The sum of number of students who opted mathematics:
\(\begin{array}{|rcll|} \hline \text{Mathematics} &=& 15+x+y+z \\ \text{Mathematics} &=& 15+41+4+4 \\ \mathbf{\text{Mathematics}} &=& \mathbf{64} \\ \hline \end{array} \)
The sum of number of students who didn't opted any of the subjects given:
\(\begin{array}{|rcll|} \hline \text{didn't opted any} &=& 120-(9+15+16+x+y+z+t) \\ \text{didn't opted any} &=& 120-(40+41+4+4+26) \\ \text{didn't opted any} &=& 120-115 \\ \mathbf{\text{didn't opted any}} &=& \mathbf{5} \\ \hline \end{array}\)
